Solve the System of Linear Equations $\left\{ \begin{array} { l l } - 8 x + 24 y + 8 z & = 5 \\ 16 x + 40 y & = 10 \\ 24 x + 8 y - 16 z & = - 5 \end{array} \right.$

Multiple Choice

Solve the system of linear equations $\left\{ \begin{array} { l l } - 8 x + 24 y + 8 z & = 5 \\ 16 x + 40 y & = 10 \\ 24 x + 8 y - 16 z & = - 5 \end{array} \right.$ using an inverse matrix.

A) $\left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { c } - \frac { 5 } { 8 } \\ 0 \\ \frac { 15 } { 8 } \end{array} \right]$

B) $\left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { c } 0 \\ \frac { 5 } { 4 } \\ - \frac { 5 } { 8 } \end{array} \right]$

C) $\left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { c } \frac { 5 } { 8 } \\ - \frac { 15 } { 8 } \\ \frac { 5 } { 4 } \end{array} \right]$

D) $\left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { c } \frac { 5 } { 8 } \\ 0 \\ \frac { 5 } { 4 } \end{array} \right]$

E) $\left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { c } - \frac { 5 } { 8 } \\ - \frac { 15 } { 8 } \\ - \frac { 5 } { 4 } \end{array} \right]$